But when we say these words to someone, they can mean much more if our hearts are truly invested in them.
This expression is not just something "nice" to say to people. It is a possibility for love that has been opened to us by the death and resurrection of Jesus. Far more important than saying "I'll pray for you" is the actual praying, of which these words form the beginning.
And the vitality of our prayer comes from the love we bring before God for the mystery of that person's life. When we pray as Christians for another person, we recognize and affirm our unity with that person in Christ's body, in which the fulfillment of all things has "already" been radically achieved and is being carried out in space and time "mystically" (which is to say "really," in the most profound sense).
When we take up another's needs as our own and bring them before God, we in some sense participate in Christ's redemption. The Holy Spirit unites us with Jesus and joins our prayer to His pouring out of Himself in love on the cross which applies to every place and time, every circumstance, every person in the history of the world. It is God's will that we might really share in the love of Christ's heart, in His ardent desire and His particular attention to the person we pray for.
This an essential, though incomprehensible, dimension of how prayer "works" in God's plan for each person and for the whole world. This is the reality of the body of Christ "extended" through all time, the unfolding through history and through our lives together of the victory of His resurrection.